Related papers: A unified multi-phase and multi-material formulati…
Resonant modes determine the response of electromagnetic devices, including dielectric and plasmonic resonators. Relying on the degrees of freedom that metamaterials provide, this contribution shows how to design, at will, the resonant…
Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modelling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the…
In this work, we demonstrate a framework for developing closure models in turbulent combustion using experimental multi-scalar measurements. The framework is based on the construction of conditional means and joint scalar PDFs from…
A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution…
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
Ultracold quantum gases provide a unique setting for studying and understanding the properties of interacting quantum systems. Here, we investigate a multi-component system of $^{87}$Rb--$^{39}$K Bose-Einstein condensates (BECs) with…
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…
Liquid crystal elastomers (LCEs) are rubber-like solids that incorporate nematic mesogens (stiff rod-like molecules) as a part of their polymer chains. In recent years, isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) has…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural…
We derive a continuum-level plasticity model for polycrystalline materials in the high energy density regime, based on a single dislocation density and single mobility mechanism, with an evolution model for the dislocation density. The…
Developing a bottom-up (molecular) theory for the electromechanical response of aperiodic materials is a prerequisite for understanding the piezoelectric properties of systems such as nanoparticles, (non-crystalline) polymers, or…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical behavior is inherently connected to fracture processes…